spin structure of the nucleon introduction to polarised dis prerequisites quark polarisation the...

Spin structure of the Spin structure of the nucleonnucleon

• introduction to polarised DIS

• prerequisites

• quark polarisation

• the (spin) structure of the nucleon

Delia Hasch

• gluon polarisation

fascinatedfascinated by spin ….by spin ….“You think you understand something? Now add spin…” -- R. Jaffe

W. Pauli

N. Bohr

preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon

Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05



what is spin ?what is spin ?[www.markusehrenfried.de/science/physics/whatisspin.html]

• Stern-Gerlach (1921):

• Uhlenbeck, Goudsmit: (1925) explanation of atomic spectra

quantum number: ms=1/2

Pauli : exclusion principle

how to study the nucleon structure how to study the nucleon structure ??

… deep-inelastic scattering (DIS)

)cos(12EE'qQlab

22 -

E'Eνlab

,2Mν

Qx

2lab

• “deep” high resolution: 22 MQ

1MM 22X x• “inelastic”

nucleon has a structure

Q2 determines the resolution



the nucleon spin structurethe nucleon spin structure

1 Σvv ΔdΔu

2

1

2

1

EMC 1988: =0.123 ± ...

QPM:

Spin Puzzle

don’t forget the orbital angular momentum!

SLAC, CERN, DESY: 0.2-0.4

0.7

)du(2

1

2

1vv

gluons are important !Gsea quarks: qs

G )qdu(2

1

2

1svv Gqsvv LL)qdu(

2

1

2

1

G



helicity densities helicity densities qq because of helicity conservation, the virtual photon can

couple only to a quark of opposite helicity

2

3SS Nγ

)(2/3 xq by changing the orientation of target nucleon spin or the

helicity of incident lepton beam we can select q(x) or q(x) q

2

1SS Nγ

)(2/1 xq





pure nuclear-polarised atomic gas, flipped at 90s time intervals, <Pt>~0.85 ±0.04

Stern-Gerlach separation

27.5 GeV (e/e)

<Pb>~ 0.53±0.03self-polarised electrons: e

Stern-Gerlach separation

• resolution: p/p~2%, <1 mrad

• particle ID: lepton ID with ~98%, hadron contamination <1%

RICH: , K, p ID within 2<Eh<15 GeV

experimental prerequisites experimental prerequisites (Hermes)(Hermes)

μνWhadronic part of the cross section contains information on nucleon structure cannot be calculated from first principles

DIS cross section DIS cross section

μνL leptonic part of the cross section independent of nucleon structure can be calculated explicitely

)XN( l'l

μνμν'

2

WLdEd

d



hadronic tensorhadronic tensor μνWparametrised by structure functions (symmetry considerations, conservation laws)

)Q(x,Fν

pp)Q(x,FW 2

2

νμ2

1μν

μν g

)Q(x,gqpSqSp

ν

1)Q(x,gS

ν

qiε 2

2σσ2

1σλμνλσ

helicity distribution of quarks

i i i

2ii

2i1 (x)Δqe

2

1(x)q(x)qe

2

1(x)g

momentum distribution of quarks

i i iiii xqexqxqexF )(

2

1)()(

2

1)( 22

1

QPM:



how to measure cross sections /how to measure cross sections /asymmetriesasymmetries

)Qx,()E'θ,( 2

E’ = const.

= const.

L

)Qx,(N)Qx,(

2)(2





quark helicity distributionsquark helicity distributions

2

1SS Nγ

)(2/1 xq

2

3SS Nγ

)(2/3 xq

2/32/11(x)g

(x)q(x)q (x)q(x)qe2

1qqe

2

1(x)g

q q

2q

2q1

q

22q

2LO1 )Qq(x,e

2

1)Q,(xg

one step further (evolution equations):

parameterised

data 2stat

2calc1

meas12 )(

gg

minimisation :

2χ

evaluate parameters

])Q,(G)Qq(x,[e2

1

2)Q,( g

2qq

22q

sLO1

2NLO1 CxCgxg

q and q and G from inclusive data G from inclusive data (QCD fit)(QCD fit)





q q and and G G from inclusive datafrom inclusive data

• uv and dv (quite) well determined: uv >0, dv <0

])Q,(G)Qq(x,[e2

1

2)( g

2qq

22q

sLO1

NLO1 CxCgxg

• q and G weakly constraint by data



how to further proceed ?how to further proceed ?

• q and q and G from inclusive G from inclusive

DIS data: viaDIS data: via evolution evolution

equationsequations requires wide kinematic range in Q2 and x

unpolarised DIS

only fixed target spinexperiments so far …

need polarised collider to

extend kinematic

coverage need more direct probes

polarised semi-inclusive DISpolarised semi-inclusive DIS

- udK- us

flavour tagging

+ ud

f

fff zDdxqz )()()(d hqh , z=Eh/

probability that struck quark

of flavour f fragments into

hadron of type h with energy fraction z

distributionfunction

fragmentationfunction





flavour content of final state hadronsrelated to flavour of struck quark viafragmentation functions

polarised quark distributionspolarised quark distributions

q

2hq

22q

q

2hq

22q

h23

h21

h23

h212h

1)Q(z,Ddz)Q(x,qe

)Q(z,Ddz)Q(x,Δqe

σσ

σσ)Q(x,A )Q,(

q

q

),(hqP

(z)Ddz)Q(x,q'e

(z)Ddz)Q(x,qe)Q(x,A 2

qq'

hq'

22q'

hq

22q2h

1 x

zx

QPA

0

s

s,

s

s,

d

d,

u

u,

d

d,

u

uQ

Dqh not well known at √s~5-20 GeV of

current polarised DIS experiments

flavour separation by flavour tagging

measured hadron measured hadron asymmetriesasymmetries

h+

-

+

h-

incl

proton

deuteron

h+

h-

+

-

K+

K-

K us all sea objects

-h-incl

x

x

Kd1,

πd1,

πp1,

d1

p1 A,A,A,A,AA



HERMES

HERMES

puritiespurities

K+

K

u u d sd s

probability that * hit a quark of flavour q when hadron of type h was detected



quark/anti-quark helicity quark/anti-quark helicity distributionsdistributions

u quarks large positive polarisation

d quarks negative polarisation

[HERMES, PRL92(2004), PRD71(2005)]

first direct 5-flavour separation of

polarised PDFs new data from COMPASS/RHIC coming

sea quarks (u, d, s ,s) compatible

with 0

- - -



how to measure the gluon how to measure the gluon polarisation polarisation G G

…reminder: from scaling violation



Gqsvv LL)qdu(2

1

2

1

G

direct measurement of direct measurement of GG method: photon-gluon fusion

t ħ/2mq

q

q

cg

c

cD

D

experimentally very challenging:

vertex reconstructioninside massive target S/B



theoretically very clean:

G

ΔGA

NN

NNA ccγp

cccc

cccc||

open charm production(hard scale: mass of c-quark)

direct measurement of direct measurement of GG method: photon-gluon fusion

t ħ/2mq

q

q

hadron pairs with high transv.momenta (hard scale: PT)

g

h1

h2



experimentally very clean

highly model dependent



GG from high-pfrom high-pTT hadron pairs hadron pairs3 main contributions to *p hh X :

pq

q

q

q q

q

V

h2

h1h1

h1

h2

h2

* **

g

g

QCDC VMD PGFAQCDC ~ q/q

estimate their relative contributions: Monte Carlo…

APGF G/GAVDM = 0

G

ΔGa

G

ΔG)qqg(γaA PGFPGF

q

Δqa

q

Δqqg)q(γaA QCDCQCDC

i PGFPGFQCDCQCDCii|| )AA(AA fff

-1

0.5



GG from high-pfrom high-pTT hadron pairs hadron pairs3 main contributions to *p hh X :

pq

q

q

q q

q

V

h2

h1h1

h1

h2

h2

* **

g

g

QCDC VMD PGFAQCDC ~ q/q APGF G/GAVDM = 0

i PGFPGFQCDCQCDCii|| )AA(AA fff

[PRL84(2000)]

GG from high-pfrom high-pTT hadron pairs hadron pairs

first glimpse:



GG from high-pfrom high-pTT hadron pairs hadron pairs

first glimps:



complementary measurement @RHIC

GG from from 00 at RHIC at RHIC



pp 0X is sensitive to gg gg and gq gq

STAR

GG from from 00 at RHIC at RHIC



pp 0X is sensitive to gg gg and gq gq

gqgq G

G

q

q

qqqqq

q

q

q

gggg G

G

G

G

fractional contributions:

• uncertainty still large ... • dramatic improvement by lumi and beam polarization (~70%)

futurefuture GG measurements (2010)measurements (2010)

first glimps:



COMPASS COMPASS :: open charm

high PT

HERMES HERMES :: high PT on d

RHIC RHIC :: 0

jets

prompt charm/bottom

where do we standwhere do we stand the (spin) structure of the nucleon …

NMC,BCDMS,E665,

H1, ZEUS

HERMES(SMC, SLAC) Compass RHIC

HERMES:first glimpse

COMPASSRHIC

? preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon


?transversity

seminar by its own

HERMESCOMPASSRHICJLabKEK …ecc.

exclusive processesfirst results:HERMESJLab

seminar by its own

the nucleon puzzle is goingthe nucleon puzzle is goingto be completedto be completed

spin structure of the nucleon introduction to polarised dis prerequisites quark polarisation the...

Documents

p h h x

gq gq g

rhic g

prl842000 g

hadron of type h

quark of flavour q

nucleon structure

quark of opposite helicity